Abstract
The concept of the RG was originally introduced in the context of quantum field theory by Stueckelberg and Petermann (1953) and by Gell-Mann and Low (1954), long before Wilson’s seminal works. Although the field-theoretical RG is less general than the Wilsonian RG and can only be applied to so-called renormalizable theories (we shall explain in this chapter what this means), calculations beyond the leading order in the number of loop integrations are usually simpler within the field theoretical RG if it is applicable. Here, we shall briefly introduce the main ideas of the field-theoretical RG method.1 More detailed introductions can be found in the authoritative book by Zinn-Justin (2002) or in many other textbooks on quantum field theory such as (Sterman 1993, Peskin and Schroeder 1995, Zee 2003).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M. and I. A. Stegun (1965), Handbook of Mathematical Functions, Dover, New York.
Creutz, M. (1983), Quarks, Gluons and Lattices, Cambridge University Press, New York.
Gell-Mann, M. and F. E. Low (1954), Quantum electrodynamics at small distances, Phys. Rev. 95, 1300.
Hewson, A. C. (1993), The Kondo Problem to Heavy Fermions, Cambridge University Press, New York.
Ledowski, S. and P. Kopietz (2007), Fermi surface renormalization and confinement in two coupled metallic chains, Phys. Rev. B 75, 045134.
Ledowski, S., P. Kopietz, and A. Ferraz (2005), Self-consistent Fermi surface renormalization of two coupled Luttinger liquids, Phys. Rev. B 71, 235106.
Neumayr, A. and W. Metzner (2003), Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model, Phys. Rev. B 67, 035112.
Nozières, P. (1964), Theory of Interacting Fermi Systems, Benjamin, New York.
Peskin, M. E. and D. V. Schroeder (1995), An Introduction to Quantum Field Theory, Addison-Wesley, Reading, MA.
Sterman, G. (1993), An Introduction to Quantum Field Theory, Cambridge University Press, Cambridge.
Stueckelberg, E. C. G. and A. Petermann (1953), La normalisation des constantes dans la théorie des quanta, Helv. Phys. Acta 26, 499.
Zee, A. (2003), Quantum Field Theory in a Nutshell, Princeton University Press, Princeton, NJ.
Zinn-Justin, J. (2002), Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford, 4th ed.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kopietz, P., Bartosch, L., Schütz, F. (2010). Field-Theoretical Renormalization Group. In: Introduction to the Functional Renormalization Group. Lecture Notes in Physics, vol 798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05094-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-05094-7_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05093-0
Online ISBN: 978-3-642-05094-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)